First slide

Trigonometric equations

Question

The set of all $x$ in $(\frac{- π}{2}, \frac{π}{2})$ satisfying $|4 \sin x - 1| < \sqrt{5}$ is given by

Moderate

A

$(\frac{- π}{10}, \frac{3 π}{10})$
B

$(\frac{- π}{10}, \frac{π}{5})$
C

$(\frac{- π}{10}, \frac{3 π}{5})$
D

$(\frac{- π}{5}, \frac{3 π}{10})$

Solution

$W e h a v e - \sqrt{5} < 4 \sin x - 1 < \sqrt{5}$
$\Rightarrow - \frac{(\sqrt{5} - 1)}{4} < \sin x < \frac{\sqrt{5} + 1}{4}$
$\Rightarrow - \sin \frac{π}{10} < \sin x < \sin \frac{3 π}{10}$
$\Rightarrow \frac{- π}{10} < x < \frac{3 π}{10}$

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